rbf.m

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%RBF Radial Basis Function algorithm
%
%   'ifile.mat' - input file containing:
%      Nr - members of ensemble
%      dim - iterations
%      Nneur - number of neurons
%      Sx - standard deviation of input
%      Sn - standard deviation of measurement noise
%      ur - convergence factor for reference vector
%      uw - convergence factor for coefficient vector
%      us - convergence factor for spread
%
%   'ofile.mat' - output file containing:
%      MSE - mean-square error


clear all		% clear memory
load ifile;		% read input variables


for j=1:Nr
   n=Sn*randn(dim,1);           % noise at channel output 
   x=Sx*randn(dim,1);     % input signal
   xl1=zeros(dim,1); xl2=xl1;
   xl1(1)=0; xl1(2:dim)=x(1:dim-1);
   xl2(1)=0; xl2(2:dim)=xl1(1:dim-1); 
   d=-.08*x-.15*xl1+.14*xl2+.055*x.^2+.3*x.*xl2-.16*xl1.^2+.14*xl2.^2+n; ...
     % unknown system output
   w=randn(Nneur,dim); w(:,1)=randn(Nneur,1);  % initial coefficient vector
   vet=.5*randn(Nneur,3);                      % initial reference vector
   sigma=ones(Nneur,1);                        % initial neuron spread
   for i=1:dim
      uxl(:,i)=[x(i) xl1(i) xl2(i)]';      % new input vector
      dis=dist(uxl(:,i)',vet')';
      fdis=exp(-(dis.^2)./(sigma.^2));
      e(i)=d(i)-w(:,i)'*fdis;              % error sample
      w(:,i+1)=w(:,i)+2*uw*e(i)*fdis;      % new coefficient vector
      sigma=sigma+2*us*e(i)*fdis.*w(:,i).*(dis.^2)./(sigma.^3); % new spread 
      for p=1:Nneur
        vet(p,:)=vet(p,:)+2*ur*fdis(p)*e(i)*w(p,i)*(uxl(:,i)'-vet(p,:))/ ...
		 (sigma(p)^2); % new reference vector
     end
     y(i)=w(:,i)'*fdis;                    % output sample
   end
   mse(j,:)=e.^2;
end

MSE=mean(mse);
save ofile MSE;